BUSCADOR RECOLECTA

Summary The note presents an output feedback control strategy for Markov jump linear systems with no mode observation. Based on minimizing a finite-time quadratic cost, we derive an algorithm that generates output feedback gains that satisfy a necessary optimality condition. These gains can be computed off-line relying only on the initial condition of the system. This result expands a previous one from the literature that considered state-feedback only. To illustrate the usefulness of the…

Fragmentation and growth-fragmentation equations is a family of problems with varied and wide applications. This paper is devoted to the description of the long-time asymptotics of two critical cases of these equations, when the division rate is constant and the growth rate is linear or zero. The study of these cases may be reduced to the study of the following fragmentation equation: ∂ / ∂t u(t, x) + u(t, x) = ∞ ∫ x k0 (x/y )u(t, y)dy. Using the Mellin transform of the equation, we…

We build nonuniform numerical meshes for the finite difference and finite element approximations of the one-dimensional wave equation, ensuring that all numerical solutions reach the boundary, as continuous solutions do, in the sense that the full discrete energy can be observed by means of boundary measurements, uniformly with respect to the mesh size. The construction of the nonuniform mesh is achieved by means of a concave diffeomorphic transformation of a uniform grid into a nonuniform one…

We derive Hardy-type inequalities for a large class of sub-elliptic operators that belong to the class of $\Delta_{\lambda}$-Laplacians and find explicit values for the constants involved. Our results generalize previous inequalities obtained for Grushin-type operators (Formula presented.) which were proved to be sharp.

We analyze a model optimal control problem for a 2D scalar conservation law-the so-called inverse design problem-with the goal being to identify the initial datum leading to a given final time configuration. The presence of shocks is an impediment for classical methods, based on linearization, to be directly applied. We develop an alternating descent method that exploits the generalized linearization that takes into account both the sensitivity of the shock location and of the smooth components…

This article is devoted to the analysis of control properties for a heat equation with a singular potential μ/δ2, defined on a bounded C2 domain Ω⊂RN, where δ is the distance to the boundary function. More precisely, we show that for any μ≤1/4 the system is exactly null controllable using a distributed control located in any open subset of Ω, while for μ>1/4 there is no way of preventing the solutions of the equation from blowing-up. The result is obtained applying a new Carleman estimate.

We analyze the null controllability for heat equations in the presence of switching controls. The switching pattern is a priori unknown so that the control has to be designed in a robust manner, based only on the past dynamics, so to fulfill the final control requirement, regardless of what the future dynamics is. We prove that such a robust control strategy actually exists when the switching controllers are located on two non trivial open subsets of the domain where the heat process evolves.…

In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the coefficient showing that dispersion occurs if this variation is small enough but it may fail when the variation goes beyond a sharp threshold. For the Schrödinger equation we prove that the dispersion holds under the same smallness assumption on the variation of the…

The homogeneous bosonic Nordheim equation is a kinetic equation describing the dynamics of the distribution of particles in the space of moments for a homogeneous, weakly interacting, quantum gas of bosons. We show the existence of classical solutions of the homogeneous bosonic Nordheim equation that blow up in finite time. We also prove finite time condensation for a class of weak solutions of the kinetic equation.

We derive homogenized von Kármán shell theories starting from three dimensional nonlinear elasticity. The original three dimensional model contains two small parameters: the period of oscillation $\epsilon$ of the material properties and the thickness $h$ of the shell. Depending on the asymptotic ratio of these two parameters, we obtain different asymptotic theories. In the case $h<<\epsilon$ we identify two different asymptotic theories, depending on the ratio of $h$ and $\epsilon^2$. In…

One of the main difficulties in the modeling and numerical simulation of the spread of an infectious disease in wildlife resides in properly taking into account the heterogeneities of the landscape. Forests, plains and mountains present different levels of hospitality, while large interstates, lakes and major waterways can provide strong natural barriers to the epidemic spread. A canonical approach has been to discretize both population and geography into geopolitical units and consider the…

Radiofrequency catheter ablation (RFCA) is an important curative treatment for cardiac arrhythmias. However, during RFCA thrombus formation can occur when the electrode-tissue interface temperature exceeds 80°C. Open-irrigated electrodes reduce the risk of such side-effect. No computational model of an open-irrigated electrode in endocardial RFCA accounting for both the saline irrigation flow and the blood motion in the cardiac chamber has been proposed yet. Our aim was to introduce the first…

Our aim was to compare the different methods of modeling the effect of circulating blood flow on the thermal lesion dimensions created by radio frequency (RF) cardiac ablation and on the maximum blood temperature. Computational models were built to study the temperature distributions and lesion dimensions created by a nonirrigated electrode by two RF energy delivery protocols (constant voltage and constant temperature) under high and low blood flow conditions. Four methods of modeling the…

[No abstract available]

The resting brain dynamics self-organize into a finite number of correlated patterns known as resting-state networks (RSNs). It is well known that techniques such as independent component analysis can separate the brain activity at rest to provide such RSNs, but the specific pattern of interaction between RSNs is not yet fully understood. To this aim, we propose here a novel method to compute the information flow (IF) between different RSNs from resting-state magnetic resonance imaging. After…

In previous studies, migraine patients showed abnormalities in pain-related evoked responses, as reduced habituation to repetitive stimulation. In this study, we aimed to apply a novel analysis of EEG bands synchronization and directed dynamical influences under painful stimuli in migraine patients compared to non-migraine healthy volunteers. Thirty-one migraine without aura outpatients (MIGR) were evaluated and compared to 19 controls (CONT). The right hand was stimulated by means of 30…

Cortical spreading depression (CSD), a depolarization wave which originates in the visual cortex and travels toward the frontal lobe, has been suggested to be one neural correlate of aura migraine. To the date, little is known about the mechanisms which can trigger or stop aura migraine. Here, to shed some light on this problem and, under the hypothesis that CSD might mediate aura migraine, we aim to study different aspects favoring or disfavoring the propagation of CSD. In particular, by using…

We design two parallel schemes, based on Schwarz Waveform Relaxation (SWR) procedures, for the numerical solution of the Kolmogorov equation. The latter is a simplified version of the Fokker-Planck equation describing the time evolution of the probability density of the velocity of a particle. SWR procedures decompose the spatio- temporal computational domain into subdomains and solve (in parallel) subproblems, that are coupled through suitable conditions at the interfaces to recover the…

The brain exhibits a wide variety of spatiotemporal patterns of neuronal activity recorded using functional magnetic resonance imaging as the so-called blood-oxygenated-level-dependent (BOLD) signal. An active area of work includes efforts to best describe the plethora of these patterns evolving continuously in the brain. Here we explore the third-moment statistics of the brain BOLD signals in the resting state as a proxy to capture extreme BOLD events. We find that the brain signal exhibits…

Brain Functional Connectivity (FC) quantifies statistical dependencies between areas of the brain. FC has been widely used to address altered function of brain circuits in control conditions compared to different pathological states, including epilepsy, a major neurological disorder. However, FC also has the as yet unexplored potential to help us understand the pathological transformation of the brain circuitry. Our hypothesis is that FC can differentiate global brain interactions across a time…

In this thesis we highlight the necessity of employing numerical schemes that preserve the large-time dynamical properties of the continuous system. We focus on Burgers- like equations, which are well known to develop N-waves as intermediate or asymptotic profiles. As we show, not only forward simulations can be distorted; the efficiency of solutions of optimization and inverse design problems might be affected too. In particular, we apply our results to the case of the prediction and control…

In this thesis we analyze the properties of controllability and observability for selected partial differential equations which model various phenomena in cardiology, biology, fluid mechanics and viscoelasticity. We begin, in chapter 2, with the analysis of the uniform controllability of families of linear coupled parabolic systems approximating parabolic-elliptic systems. We prove, under appropriate assumptions on the coupling terms, the uniform, with respect to the degenerating parameter,…

In this thesis new numerical methods are presented for the analysis of models in population dynamics. The methods approximate equilibria and bifurcations in a certain class of so called structured population models. Chapter 1 consists of an introduction to structured population dynamics, where the state of the art is presented through a classical consumer-resource model [44]. The necessity of new numerical methods for analyzing structured population models is discussed and motivated by their…

The magnetotelluric (MT) method is a passive exploration technique that aims at esti- mating the resistivity distribution of the Earth’s subsurface, and therefore at providing an image of it. This process is divided into two different steps. The first one consists in recording the data. In a second step, recorded measurements are analyzed by employing numerical methods. This dissertation focuses in this second task. We provide a rigorous mathematical setting in the context of the Finite Element…

We present a new mathematical theory explaining the fluid mechanics of subsonic flight, which is fundamentally different from the existing boundary layer-circulation theory by Prandtl–Kutta–Zhukovsky formed 100 year ago. The new theory is based on our new resolution of d’Alembert’s paradox showing that slightly viscous bluff body flow can be viewed as zero-drag/lift potential flow modified by 3d rotational slip separation arising from a specific separation instability of potential flow, into…

Mortality data provide valuable information for the study of the spatial distri- bution of mortality risk, in disciplines such as spatial epidemiology and public health. However, they are frequently available in an aggregated form over irreg- ular geographical units, hindering the visualization of the underlying mortality risk. Also, it can be of interest to obtain mortality risk estimates on a finer spatial resolution, such that they can be linked to potential risk factors that are usually…

With the aim of applying numerical methods, we develop a formalism for physiologically structured population models in a new generality that includes con- sumer resource, cannibalism and trophic models. The dynamics at the population level are formulated as a system of Volterra functional equations coupled to ODE. For this general class we develop numerical methods to continue equilibria with respect to a parameter, detect transcritical and saddle-node bifurcations and compute curves in…

In this paper we propose a new algorithm for the well known elliptic obstacle problem and for parabolic variational inequalities like one and two phase Stefan problem and of obstacle type. Our approach enters the category of fixed domain methods and solves just linear elliptic or parabolic equations and their discretization at each iteration. We prove stability and convergence properties. The approximating coincidence set is explicitly computed and it converges in the Hausdorff-Pompeiu sense to…

Due to the progressive growth of the amount of data available in a wide variety of scientific fields, it has become more difficult to manipulate and analyze such information. In spite of its dependency on the initial settings and the large number of distance computations that it can require to converge, the $K$-means algorithm remains as one of the most popular clustering methods for massive datasets. In this work, we propose an efficient approximation to the $K$-means problem intended for…, Marco Capó and Aritz Pérez are partially supported by the Basque Government, Elkartek and by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excelence accreditation SVP-2014- 068574 and SEV-2013-0323. José A. Lozano is partially supported by the Basque Government (IT609-13), Elkartek and the Spanish Ministry of Economy and Competitiveness MINECO (TIN2013-41272P).

The complex, highly individual, geometry of the cerebral cortex in humans presents a major challenge in studying the spreading of spontaneous neuronal activity. Recent computational advances [1] allow to simulate the propagation of depolarization waves on the macroscale and for individual geometries, reconstructed from accurate medical imaging as MRI, with high levels of detail. In this paper we take advantage of such technique to study the temporal excitation patterns that follow the passage…, This work was supported by the Bizkaia Talent and European Commission through COFUND under the grant BRAhMS – Brain Aura Mathematical Simulation– (AYD-000- 285), and also by the Basque Government through the BERC 2014-2017 program, and by the Spanish Ministry of Economics and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323. JMC acknowledges financial support from Ikerbasque: The Basque Foundation for Science and Euskampus at UPV/EHU.

Cortical Spreading Depression (CSD), a depolarization wave originat- ing in the visual cortex and traveling towards the frontal lobe, is com- monly accepted as a correlate of migraine visual aura. As of today, little is known about the mechanisms that can trigger or stop such phenomenon. However, the complex and highly individual characteristics of the brain cortex suggest that the geometry might have a significant impact in sup- porting or contrasting the propagation of CSD. Accurate patient-…, This work was supported by the Bizkaia Talent and European Commission through COFUND under the grant BRAhMS - Brain Aura Mathematical Sim- ulation (AYD-000-285), by the Basque Government through the BERC 2014- 2017 program, and by the Spanish Ministry of Economics and Competitiveness MINECO through the BCAM Severo Ochoa excellence accreditation SEV-2013- 0323 and the Spanish "Plan Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad" under Grant…

In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$-interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing into fibers, we prove that there is discrete spectrum only in dimension three and that it is generated by the axisymmetric fiber. We get that these eigenvalues are nondecreasing functions of the aperture of the cone and we exhibit the precise logarithmic accumulation of the…, V.Lotoreichik is supported by the Czech Science Foundation (GACˇR) under the project 14-06818S. He is grateful for the stimulating research stay and the hospitality at the Basque Center for Applied Mathematics in May 2015 where a part of this paper was written.

In this paper we study mixed weighted weak-type inequal- ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2].

Before the use of a diagnostic test in a routine clinical setting, the rigorous evaluation of its diagnostic accuracy is an essential step. The receiver operating characteristic (ROC) curve is the measure of accuracy most widely used for continuous diagnostic tests. However, the possible impact of extra information about the patient (or even the environment) on diagnostic accuracy needs to be also assessed. In this paper, attention is focused on an estimator for the covariate-specific ROC curve…

We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calderón-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by Sawyer estimating the $L^{1,\infty}(uv)$ norm of $v^{−1}T(fv)$ for special cases. The emphasis is made in proving new and more precise quantitative estimates involving the $A_p$ or $A_{\infty}$ constants of the weights involved.

We present dimension-free reverse Hölder inequalities for strong $A^{\ast}_p$ weights, $1 \le p < \infty$. We also provide a proof for the full range of local integrability of $A^{\ast}_1$ weights. The common ingredient is a multidimensional version of Riesz’s “rising sun” lemma. Our results are valid for any nonnegative Radon measure with no atoms. For $p = \infty$, we also provide a reverse Ho ̈lder inequality for certain product measures. As a corollary we derive mixed $A^{\ast}_p − A^{\…, The third author is partially supported by grants UBACyT 20020130100403BA, and PIP (CONICET) 11220110101018.

We introduce a new method that approximates free-form surfaces by envelopes of one-parameter motions of surfaces of revolution. In the context of 5-axis computer numerically controlled (CNC) machining, we propose a flank machining methodology which is a preferable scallop-free scenario when the milling tool and the machined free-form surface meet tangentially along a smooth curve. We seek both an optimal shape of the milling tool as well as its optimal path in 3D space and propose an…

We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature rules we recently derived [6] act on spaces of the smallest odd degrees and, therefore, are still slightly sub-optimal. In this work, we derive optimal rules directly for even- degree spaces and therefore further improve our recent result. We use optimal quadrature rules for…

In this paper we establish the following estimate \[ w\left(\left\{ x\in\mathbb{R}^{n}\,:\,\left|[b,T]f(x)\right| > \lambda\right\} \right)\leq \frac{c_{T}}{\varepsilon^{2}}\int_{\mathbb{R}^{n}}\Phi\left(\|b\|_{BMO}\frac{|f(x)|}{\lambda}\right)M_{L(\log L)^{1+\varepsilon}}w(x)dx \] where $w\geq0, \, 0<\varepsilon<1$ and $\Phi(t)=t(1+\log^+(t))$. This inequality relies upon the following sharp $L^p$ estimate \[ \|[b,T]f\|_{L^{p}(w)}\leq c_{T}\left(p'\right)^{2}p^{2}\left(\frac{p-1…

We obtain the off-diagonal Muckenhoupt-Wheeden conjecture for Calderón-Zygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the Hardy-Littlewood maximal function satisfies the following two weight inequalities: $$ M:L^p(v) \to L^q(u) \quad \mbox{and} \quad M: L^{q'} (u^{1-q'}) \to (v^{1-p'} ); $$ then any Calderón-Zygmund operator $T$ and its associated truncated maximal operator $T_{*}$ are bounded from $M:L^p(v)$ to $L^q(u)$.…

Three observations on commutators of Singular Integral Operators with BMO functions are exposed, namely 1 - The already known subgaussian local decay for the commutator, namely $\[\frac{1}{|Q|}\left|\left\{x\in Q\, : \, |[b,T](f\chi_Q)(x)|>M^2f(x)t\right\}\right|\leq c e^{-\sqrt{ct\|b\|_{BMO}}}\]$ is sharp, since it cannot be better than subgaussian. 2 - It is not possible to obtain a pointwise control of the commutator by a finite sum of sparse operators defined by $L\log L$ averages…, MTM2012-30748

We consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an Aharonov-Bohm magnetic field supported on the axis of symmetry and Dirichlet boundary conditions on the boundary of the domain. We show that there exists a critical total magnetic flux depending on the aperture of the conical surface for which the system undergoes an abrupt spectral transition from infinitely many eigenvalues below the essential spectrum to an empty discrete spectrum.…

During the production process of beer, it is of utmost importance to guarantee a high consistency of the beer quality. For instance, the bitterness is an essential quality parameter which has to be controlled within the specifications already at the beginning of the production process in the unfermented beer (wort) as well as in final products such as beer and beer mix beverages. Nowadays, analytical techniques for quality control in beer production are mainly based on manual supervision, i.e.…

We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain convolution operation: the latter maps a classical probability distribution on phase space and a quantum state to a quantum state. We show that this inequality also gives rise to several related inequalities whose counterparts are well-known in the classical…

Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \|T_\Omega \|_{L^p(w)}\le c_{n,p}\|\Omega\|_{L^\infty} [w]_{A_1}^{\frac{1}{p}}\,[w]_{A_{\infty}}^{1+\frac{1}{p'}}\|f\|_{L^p(w)} \] and \[ \| [b,T_{\Omega}]f\| _{L^{p}(w)}\leq c_{n,p}\|b\|_{BMO}\|\Omega\|_{L^{\infty}} [w]_{A_1}^{\frac{1}{p}}[w]_{A_{\infty}}^{2+\frac{1}{p'}}\|f…

An important aim of the analysis of agricultural field trials is to obtain good predictions for genotypic performance, by correcting for spatial effects. In practice these corrections turn out to be complicated, since there can be different types of spatial effects; those due to management interventions applied to the field plots and those due to various kinds of erratic spatial trends. This paper presents models for field trials in which the random spatial component consists of tensor product…

We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem for the anomalous diffusion equation $\partial_tu-\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ can be any nonlocal symmetric degenerate elliptic operator including the fractional Laplacian and numerical discretizations of this operator. The function $\varphi:\mathbb{R} \to \mathbb{R}$ is only assumed to be continuous and nondecreasing. The class of equations include…

In this paper we extend Sylvester's approach via upper triangular compact operators to establish the discreteness of transmission eigenvalues for higher-order main terms and higher-order perturbations. The coefficients of the perturbations must be sufficiently smooth and the coefficients of the higher-order terms of the perturbation must vanish in a neighborhood of the boundary of the underlying domain. The zeroth-order term must satisfy a suitable coercivity condition in a neighborhood of…

The Lotka-Volterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting both species as the control variable. We analyse the optimal hunting problem paying special attention to the nature of the optimal state and control trajectories in long time intervals. To do that, we apply recent theoretical results on the frame to show that, when the time…

We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for SL(3,Z), and as an application obtain a pointwise estimate and a second moment estimate for the sums in question.

In this paper, following Nachman's idea [14] and Haberman and Tataru's idea [9], we reconstruct $C^1$ conductivity $\gamma$ or Lipchitz conductivity $\gamma$ with small enough value of $|\nabla log\gamma|$ in a Lipschitz domain $\Omega$ from the Dirichlet-to-Neumann map $\Lambda_{\gamma}$. In the appendix the authors and R. M. Brown recover the gradient of a $C^1$-conductivity at the boundary of a Lipschitz domain from the Dirichlet-to-Neumann map $\Lambda_{\gamma}$.

Electrons and their interactions are intrinsic factors to affect the structure and properties of materials. Based on the “cluster-cluster-plus-glue-atom” model, an electron counting rule for complex metallic alloys (CMAs) has been revealed in this work (i. e. the CPGAMEC rule). Our results on the cluster structure and electron concentration of CMAs with apparent cluster features, indicate that the valence electrons’ number per unit cluster formula for these CMAs are specific constants of eight-…

The Boltzmann distribution plays a key role in the field of optimization as it directly connects this field with that of probability. Basically, given a function to optimize, the Boltzmann distribution associated to this function assigns higher probability to the candidate solutions with better quality. Therefore, an efficient sampling of the Boltzmann distribution would turn optimization into an easy task. However, inference tasks on this distribution imply performing operations over an…

The performance of local search algorithms is influenced by the properties that the neighborhood imposes on the search space. Among these properties, the number of local optima has been traditionally considered as a complexity measure of the instance, and different methods for its estimation have been developed. The accuracy of these estimators depends on properties such as the relative attraction basin sizes. As calculating the exact attraction basin sizes becomes unaffordable for moderate…

We introduce a new Adaptive Integration Approach (AIA) to be used in a wide range of molecular simulations. Given a simulation problem and a step size, the method automatically chooses the optimal scheme out of an available family of numerical integrators. Although we focus on two-stage splitting integrators, the idea may be used with more general families. In each instance, the system-specific integrating scheme identified by our approach is optimal in the sense that it provides the best…, MTM2013-46553-C3-1-P, BES-2014-068640

A parallel matheuristic algorithm is presented as a spin-off from the exact Branch-and-Fix Coordination (BFC) algorithm for solving multistage stochastic mixed 0-1 problems. Some steps to guarantee the solution’s optimality are relaxed in the BFC algorithm, such that an incomplete backward branching scheme is considered for solving large sized problems. Additionally, a new branching criterion is considered, based on dynamically-guided and stage-wise ordering schemes, such that fewer Twin Node…, MTM2015-65317-P, MTM2015-63710-P, IT928-16; UFI BETS 2011; IZO-SGI SGIker

The design of a Solar Power Tower plant involves the optimization of the heliostat field layout. Fields are usually designed to have all heliostats of identical size. Although the use of a single heliostat size has been questioned in the literature, there are no tools to design fields with heliostats of several sizes at the same time. In this paper, the problem of optimizing the heliostat field layout of a system with heliostats of different sizes is addressed. We present an optimization tool…, MTM2013-41286-P (Spain) MTM2015-65915-R (Spain) P11-FQM-7603 (Andalucía) TD1207 (EU COST Action)

Background Although subtypes of chronic obstructive pulmonary disease are recognized, it is unknown what happens to these subtypes over time. Our objectives were to assess the stability of cluster-based subtypes in patients with stable disease and explore changes in clusters over 1 year. Methods Multiple correspondence and cluster analysis were used to evaluate data collected from 543 stable patients included consecutively from 5 respiratory outpatient clinics. Results Four subtypes were…

In the last years, the complexity paradigm is gaining momentum in many research fields where large multidimensional datasets are made available by the advancements in instrumental technology. A complex system is a multi-component system with a large number of units characterized by cooperative behavior and, consequently, emergence of well-defined self-organized structures, such as communities in a complex network. The self-organizing behavior of the brain neural network is probably the most…

High-frequency trading has been experiencing an increase of interest both for practical purposes within nancial institutions and within academic research; recently, the UK Government O ce for Science reviewed the state of the art and gave an outlook analysis. Therefore, models for tick-by-tick nancial time series are becoming more and more important. Together with high-frequency trading comes the need for fast simulations of full synthetic markets for several purposes including scenario…, Economic and Social Research Council (ESRC) grant number ES/K002309/1.

In this paper, we discuss the efficiency of various numerical methods for the inverse design of the Burgers equation, both in the viscous and in the inviscid case, in long time-horizons. Roughly, the problem consists in, given a final desired target, to identify the initial datum that leads to it along the Burgers dynamics. This constitutes an ill-posed backward problem. We highlight the importance of employing a proper discretization scheme in the numerical approximation of the equation under…

Today, we are living a growing demand of larger and more efficient computational resources from the scienti c community. On the other hand, the appearance of GPUs for general purpose computing supposed an important advance for covering such demand. These devices o er an impressive computational capacity at low cost and an efficient power consumption. However, the memory available in these devices is (sometimes) not enough, and so it is necessary computationally expensive memory transfers from (…

The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. In this thesis, we show that performance of HMC can be dramatically improved by replacing Hamiltonians in the Metropolis test with modified Hamiltonians, and a complete momentum update with a partial momentum refreshment. The resulting generalized HMC importance sampler, which we called Mix & Match Hamiltonian Monte Carlo (MMHMC), arose as an extension of the Generalized…, FPU12/05209, MTM2013–46553–C3–1–P

In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a recent work of Hytönen, Roncal and Tapiola. We also derive new mixed weighted estimates for a general class of bilinear dyadic positive operators using multiple $A_\infty$ constants inspired in the Fujii-Wilson and Hrusˇcˇev classical constants. These estimates…, Analytic-probabilistic methods for borderline singular integrals; MTM2015-63699-P "Análisis Complejo, Espacios de Banach y Operadores"

We present a modelling approach for diffusion in a complex medium characterized by a random lengthscale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle tracking experiments in living cells, such as ergodicity breaking, p- variation and aging. In particular, this approach recapitulates characteristic features previously described in part by the fractional Brownian motion and in part by the continuous-time random walk. Moreover,…, SEV-2015-0522 FIS2014-56107- R, Fundació Privada CELLEX (Barcelona), HFSP (GA RGP0027/2012), LaserLab Europe 4 (GA 654148)

Aboveground biomass estimation in short-rotation forestry plantations is an essential step in the development of crop management strategies as well as allowing the economic viability of the crop to be determined prior to harvesting. Hence, it is important to develop new methodologies that improve the accuracy of predictions, using only a minimum set of easily obtainable information i.e. diameter and height. Many existing models base their predictions only on diameter (mainly due to the…

Optimization of orbital maneuvers is one of the main issues in conceptual and preliminary design of spacecraft in different space missions. The main issue in optimization of high-thrust orbit transfers is that the common optimization algorithms such as Genetic Algorithm and Simulated Annealing are not effectual in finding optimal transfer when they are purely used in optimization. In such problems, modified algorithms are required to find the optimal transfer. Such modifications involve…

We propose a new memetic strategy that can solve the multi-physics, complex inverse problems, formulated as the multi-objective optimization ones, in which objectives are misfits between the measured and simulated states of various governing processes. The multi-deme structure of the strategy allows for both, intensive, relatively cheap exploration with a moderate accuracy and more accurate search many regions of Pareto set in parallel. The special type of selection operator prefers the…

Magnetotelluric (MT) problems often contain different subdomains where the conductivity of the media depends upon one, two, or three spatial variables. Traditionally, when a MT problem incorporates a three-dimensional (3D) subdomain, the numerical method employed for simulation and inversion was 3D over then entire domain. In here, we propose to take advantage of the possibly lower dimensionality of certain subdomains during the inversion process. By doing so, we obtain significant…

Communications in mobile opportunistic networks, instead of using the Internet infrastructure, take place upon the establishment of ephemeral contacts among mobile nodes using direct communication. In this paper, we analytically model the performance of mobile opportunistic networks for contact-based messaging applications in city squares or gathering points, a key challenging topic that is required for the effective design of novel services. We take into account several social aspects such as…, TEC2014-52690-R, MTM2013-47093-P, AICO/2015/113, ACOMP/2015/005

We propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce $C^0$-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method ``refined Isogeometric Analysis (rIGA)…, The Project of the Spanish Ministry of Economy and Competitiveness MTM2016-76329-R. The Consolidated Research Group Grant IT649-13 on "Mathematical Modeling, Simulation, and Industrial Applications (M2SI)", The ICERMAR Project KK-2015/0000097.

High-Reynolds number turbulent incompressible multiphase flow represents a large class of engineering problems of key relevance to society. Here we describe our work on modeling two such problems: 1. The Consorcio de Aguas Bilbao Bizkaia is constructing a new storm tank system with an automatic cleaning system, based on periodically pushing tank water out in a tunnel 2. In the framework of the collaboration between BCAM - Basque Center for Applied Mathematics and Tecnalia R & I, the…

In diffusion nuclear magnetic resonance (NMR) and diffusion magnetic resonance imaging (MRI), the multi-compartment Bloch-Torrey equation plays an important role in probing the diffusion characteristics from a nanometer scale to a macroscopic scale. The signal attenuation can be computed by solving the equation. If the volume of interest is composed by multiple compartments, interface conditions with permeability are imposed. Depending on applications, different gradient strengths can be used…

In this thesis, we investigate controllability and observability properties of Partial Differential Equations describing various phenomena appearing in several fields of the applied sciences such as elasticity theory, ecology, anomalous transport and diffusion, material science, porous media flow and quantum mechanics. In particular, we focus on evolution Partial Differential Equations with non-local and singular terms. Concerning non-local problems, we analyse the interior controllability of…

If $x_0$ is an equilibrium of an autonomous differential equation $\dot x=f(x)$ and $\det \|f'(x_0)\|\not=0$, then $x_0$ persists under autonomous perturbations and $x_0$ transforms into a $T$-periodic solution under non-autonomous $T$-periodic perturbations. In this paper we discover a similar structural stability for Moreau sweeping processes of the form $-\dot u\in N_B(u)+f_0(u),$ $u\in\mathbb{R}^2,$ i. e. we consider the simplest case where the derivative is taken with respect to the…

Cortical Spreading Depression (CSD) is a disruption of the brain hemostasis that, originating in the visual cortex and traveling towards the frontal lobe, temporarily impairs the normal functioning of neurons. Although, as of today, little is known about the mechanisms that can trigger or stop such phenomenon, CSD is commonly accepted as a correlate of migraine visual aura. In this paper, we introduce a multiscale PDE-ODE model that couples the propagation of the depolarization wave associated…

Micromagnetic con gurations of the vortex and onion type have beenwidely studied in the context of planar structures. Recently a signi cant interest to micromagnetic curved thin lms has appeared. In particular, thin spherical shells are currently of great interest due to their capability to support skyrmion solutions which can be stabilized by curvature e ects only, in contrast to the planar case where the intrinsic Dzyaloshinsky-Moriya interaction is required.The aimof the paper is to performa…

We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a $C^2$-compact surface without boundary. To do so we are lead to study the layer potential induced by the Dirac system as well as to define traces in a weak sense for functions in the appropriate Sobolev space. Finally, we introduce Calderón projectors associated with the problem and illustrate the method in two special cases: the well-known MIT bag model and an electrostatic $\delta…, ANR-11- LABX-0056-LMH, LabEx LMH

A fast and stable algorithm for estimating multidimensional adaptive P-spline models is presented. We call it as Separation of Overlapping Penalties (SOP) as it is an extension of the Separation of Anisotropic Penalties (SAP) algorithm. SAP was originally derived for the estimation of the smoothing parameters of a multidimensional tensor product P-spline model with anisotropic penalties., MTM2014-55966-P MTM2014-52184-P

Data analysed here derive from experiments conducted to study neurons' activity in the visual cortex of behaving monkeys. We consider a spatio-temporal adaptive penalized spline (P-spline) approach for modelling the firing rate of visual neurons. To the best of our knowledge, this is the first attempt in the statistical literature for locally adaptive smoothing in three dimensions. Estimation is based on the Separation of Overlapping Penalties (SOP) algorithm, which provides the stability…, MTM2014-55966-P MTM2014-52184-P RETICS, Oftared - RD12/0034/0017

In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these invariants. A purpose of this note is to show how the conjecture arises. Because of the integral identity’s nature, we shall give a quick tour on theories of motivic integration, which lead to a proof of the conjecture for algebraically closed ground fields of characteristic zero.

We give a new proof of the $L^2$ version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of optimal Gaussian decay bounds for solutions to the heat equation with Gaussian decay at a future time.We extend the result to heat equations with lower order variable coefficient., IT641-13 (GIC12/96), DMS-0968472, DMS-1265249

Health related quality of life (HRQoL) has become an increasingly important indicator of health status in clinical trials and epidemiological research. Moreover, the study of the relationship of HRQoL with patients' and disease's characteristics has become one of the primary aims of many HRQoL studies. HRQoL scores are usually assumed to be distributed as binomial random variables and often highly skewed. The use of the beta-binomial distribution in the regression context has been…, IT-620-13, MTM2013-40941-P, MTM2014-52184-P, MTM2016-74931-P, RD12/0001/0001 - REDISSEC

Classically, there exists a determinant map from the moduli space of semi-stable sheaves on a smooth, projective variety to the Picard scheme. Unfortunately, if the underlying variety is singular, then such a map does not exist. In the case the underlying variety is a nodal curve, a similar map was produced by Bhosle on a stratification of the moduli space of semi-stable sheaves. In this note, we generalize this result to the higher dimension case.

In [Kol13] Kollár defined $i$-th index of a proper scheme over a field. In this note we study how index behaves under specialization, in any characteristic.

In this article, we study the Hilbert scheme of effective divisors in smooth hypersurfaces in $\mathbb{P}^3$, a topic not extensively studied. We prove that there exists such effective divisors $D$ satisfying the property: there exists infinitesimal deformations of $D$ not deforming the associated reduced scheme $D_{\mathrm{red}}$. We observe that such infinitesimal deformations contribute to non-reducedness of the corresponding Hilbert scheme. We finally introduce a concept of simple…

In this paper we explore the generalized Nash problem for arcs on a germ of smooth surface: given two prime divisors above its special point, to determine whether the arc space of one of them is included in the arc space of the other one. We prove that this problem is combinatorial and we explore its relation with several notions of adjacency of plane curve singularities.

[TBA]

The Alexander polynomial of a plane curve is an important invariant in global theories on curves. However, it seems that this invariant and even a much stronger one the fundamental group of the complement of a plane curve may not distinguish non-reduced curves. In this article, we consider a general problem which concerns a hypersurface of the complex projective space $\mathbb P^n$ defined by an arbitrary homogeneous polynomial $f$. The singularity of $f$ at the origin of $\mathbb C^{n+1}$ is…

This paper proposes a systematic direct approach to carry out effective multi-objective optimization of space orbit transfer with high-level thrust acceleration. The objective is to provide a transfer trajectory with acceptable accuracy in all orbital parameters while minimizing spacecraft fuel consumption. With direct control parameterization, in which the steering angles of thrust vector are interpolated through a finite number of nodes, the optimal control problem is converted into the…

We consider the two-dimensional Landau-de Gennes energy with several elastic constants, subject to general $k$-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent with the symmetry of the boundary conditions exist only in the case $k=2$. In this case we identify three types of radial profiles: with two, three of full five components and numerically investigate their minimality and stability depending on suitable parameters. We also…

For a bounded domain $\Omega\subset\mathbb{R}^m, m\geq 2,$ of class $C^0$, the properties are studied of fields of `good directions', that is the directions with respect to which $\partial\Omega$ can be locally represented as the graph of a continuous function. For any such domain there is a canonical smooth field of good directions defined in a suitable neighbourhood of $\partial\Omega$, in terms of which a corresponding flow can be defined. Using this flow it is shown that $\Omega$ can…

Studies into the impact of vaccination against the varicella zoster virus (VZV) have increasingly focused on herpes zoster (HZ), which is believed to be increasing in vaccinated populations with decreasing infection pressure. This idea can be traced back to Hope-Simpson's hypothesis, in which a person's immune status determines the likelihood that he/she will develop HZ. Immunity decreases over time, and can be boosted by contact with a person experiencing varicella (exogenous…, PIENTER2 serological study

Today, we are living a growing demand of larger and more efficient computational resources from the scientific community. On the other hand, the appearance of GPUs for general purpose computing supposed an important advance for covering such demand. These devices offer an impressive computational capacity at low cost and an efficient power consumption. However, the memory available in these devices is (sometimes) not enough, and so it is necessary computationally expensive memory transfers from…

An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring the matrix-vector product with the shifted matrix. Furthermore, the multipreconditioned search space is shown to grow only linearly with the number of preconditioners. This allows for a more efficient implementation of the algorithm. The proposed implementation…, U.S. National Science Foundation under grant DMS–1418882 and and by the Department of Energy grant DE–SC001657

We propose a semiparametric mixed–effects model (SNMM) using penalized splines to clas- sify longitudinal data and improve the prediction of a binary outcome. The work is motivated by a study in which different hormone levels were measured during the early stages of preg- nancy, and the challenge is using this information to predict normal versus abnormal pregnancy outcomes. The aim of this paper is to compare models and estimation strategies based on alternative formulations of SNMMs depending…, MTM2014-52184-P

The Cox proportional hazards model is the most widely used survival prediction model for analysing timeto-event data. To measure the discrimination ability of a survival model the concordance probability index is widely used. In this work we studied and compared the performance of two different estimators of the concordance probability when a continuous predictor variable is categorised in a Cox proportional hazards regression model. In particular, we compared the c-index and the concordance…, IT620-13 MTM2013-40941-P MTM2014-55966-P MTM2016-74931-P PEst-OE/MAT/UI0013/2014 PI020510 200111002 2005111008

We explain the properties and clarify the meaning of quantum weak values using only the basic notions of elementary quantum mechanics., MTM2013-46553-C3-1-P

The human brain is a small organ which uses a disproportional amount of the total metabolic energy pro- duction in the body. While it is well understood that the most significant energy sink is the maintenance of the neuronal membrane potential during the brain signaling activity, the role of astrocytes in the energy balance continues to be the topic of a lot of research. A key function of astrocytes, besides clearing glutamate from the synaptic clefts, is the potassium clearing after neuronal…, This work was supported by the Bizkaia Talent and European Commission through CO- FUND under the grant CIPAS: Computational Inverse Problems Across Scales (AYD-000-278, 2015), by the Basque Government through the BERC 2014-2017 program, and by the Spanish Ministry of Economics and Competitive- ness MINECO through the BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and the Spanish ”Plan Estatal de Investigacio ́n, Desarrollo e Innovacio ́n Orientada a los Retos de la Sociedad” under…

We describe a high-performance solution framework for isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built on top of PetIGA, an open-source library we have built and developed over the last decade, PetIGA-MF is a general multi-field discretization tool. To test the capabilities of our implementation, we solve different viscous flow problems such as Darcy, Stokes, Brinkman, and Navier–Stokes equations. Several convergence benchmarks based on manufactured solutions are…, National Priorities Research Program grant 7-1482-1-278 from the Qatar National Research Fund (a member of The Qatar Foundation). Agencia Nacional de Promoción Científica y Tecnológica grants PICT 2014-2660 and PICT-E 2014-019. The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin.